Question
upstudy study bank question image url

Suma o Diferencia de Cubos 7) \( x^{3}-125 \) 8) \( 8 y^{3}+27 \)

Ask by Ramirez French. in Mexico
Mar 12,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

### Soluciones Simplificadas: 1. \( x^{3} - 125 = (x - 5)(x^2 + 5x + 25) \) 2. \( 8y^{3} + 27 = (2y + 3)(4y^2 - 6y + 9) \)

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

The Deep Dive

Para el polinomio \( x^{3}-125 \), se puede reconocer como una diferencia de cubos. Puedes factorizarlo como \( (x - 5)(x^{2} + 5x + 25) \). Esto se debe a que \( 125 \) es \( 5^{3} \), así que la fórmula general para la diferencia de cubos, \( a^{3} - b^{3} = (a - b)(a^{2} + ab + b^{2}) \), te será útil aquí. En el caso de \( 8y^{3} + 27 \), este se presenta como una suma de cubos. Puedes factorizarlo usando la fórmula \( a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2}) \). Así, podemos expresar \( 8y^{3} + 27 \) como \( (2y + 3)(4y^{2} - 6y + 9) \), ya que \( 8y^{3} = (2y)^{3} \) y \( 27 = 3^{3} \).

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy